1. Find Side a using Side b=3, Angle A=60, Angle B=45 (Law of Sines)
Solution:
The law of sines states that
`a/sin(A)=b/sin(B)=c/sin(C)`
We have `b=3,A=60,B=45`
`:.a/sin(A)=b/sin(B)`
`:.a=(b*sin(A))/sin(B)`
`:.a=(3*sin(60))/sin(45)`
`:.a=(3*0.866)/(0.7071)`
`:.a=3.6742`
`A+B+C=180`
`:.C=180-(A+B)`
`:.C=180-(60+45)`
`:.C=180-105`
`:.C=75`
`c/sin(C)=b/sin(B)`
`:.c=(b*sin(C))/sin(B)`
`:.c=(3*sin(75))/sin(45)`
`:.c=(3*0.9659)/(0.7071)`
`:.c=4.0981`
perimeter `P=a+b+c=3.6742+3+4.0981=10.7723`
Area `=1/2 ab*sin(C)=1/2 *3.6742*3*sin(75)=1/2 *3.6742*3*0.9659=5.3236`
This material is intended as a summary. Use your textbook for detail explanation.
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